We study Hawking radiation from three-dimensional black holes. For this purpose the emission of charged scalar and charged fermionic particles is investigated from charged BTZ black holes, with and without rotation. We use the quantum tunneling approach incorporating WKB approximation and spacetime symmetries. Another class of black holes which is asymptotic to a Sol three-manifold has also been investigated. This procedure gives us the tunneling probability of outgoing particles, and we compute the temperature of the radiation for these black holes. We also consider the quantum tunneling of particles from black hole asymptotic to Sol geometry.

We characterize the geometric moduli of non-Khler manifolds with torsion. Heterotic supersymmetric flux compactifications require that the six-dimensional internal manifold be balanced, the gauge bundle be Hermitian YangMills, and also the anomaly cancellation be satisfied. We perform the linearized variation of these constraints to derive the defining equations for the local moduli. We explicitly determine the metric deformations of the smooth flux solution corresponding to a torus bundle over <i>K</i>3.

General relativity explains gravitational radiation from binary black hole or neutron star mergers, from core-collapse supernovae and even from the inflation period in cosmology. These waves exhibit a unique effect called memory or Christodoulou effect, which in a detector like LIGO or LISA shows as a permanent displacement of test masses and in radio telescopes like NANOGrav as a change in the frequency of pulsars' pulses. It was shown that electromagnetic fields and neutrino radiation enlarge the memory. Recently it has been understood that the two types of memory addressed in the literature aslinear'andnonlinear'are in fact two different phenomena. The former is due to fields that do not and the latter is due to fields that do reach null infinity.

Abstract Topological Quantum Field Theories (TQFTs) pertinent to some emergent low energy phenomena of condensed matter lattice models in 2+ 1 and 3+ 1 dimensions are explored. Many of our TQFTs are highly-interacting without free quadratic analogs. Some of our bosonic TQFTs can be regarded as the continuum field theory formulation of DijkgraafWitten twisted discrete gauge theories. Other bosonic TQFTs beyond the DijkgraafWitten description and all fermionic TQFTs (namely the spin TQFTs) are either higher-form gauge theories where particles must have strings attached, or fermionic discrete gauge theories obtained by gauging the fermionic Symmetry-Protected Topological states (SPTs). We analytically calculate both the Abelian and non-Abelian braiding statistics data of anyonic particle and string excitations in these theories, where the statistics data can one-to-one characterize the underlying

This paper gives a survey of wave dynamics in the Kerr space-time geometry, the mathematical model of a rotating black hole in equilibrium. After a brief introduction to the Kerr metric, we review the separability properties of linear wave equations for fields of general spin s= 0,rac {1}{2}, 1, 2, corresponding to scalar, Dirac, electromagnetic fields and linearized gravitational waves. We give results on the long-time dynamics of Dirac and scalar waves, including decay rates for massive Dirac fields. For scalar waves, we give a rigorous treatment of superradiance and describe rigorously a mechanism of energy extraction from a rotating black hole. Finally, we discuss the open problem of linear stability of the Kerr metric and present partial results.